Index: wordpress-importer.php
===================================================================
--- wordpress-importer.php	(revision 1734080)
+++ wordpress-importer.php	(working copy)
@@ -1002,7 +1002,12 @@
 			return new WP_Error( 'import_file_error', sprintf( __('Remote server returned error response %1$d %2$s', 'wordpress-importer'), esc_html($headers['response']), get_status_header_desc($headers['response']) ) );
 		}
 
-		$filesize = filesize( $upload['file'] );
+        if ( isset( $headers['content-encoding'] ) && $headers['content-encoding'] == 'gzip' ) {
+            $gzfile = gzencode( file_get_contents( $upload['file'] ) );
+            $filesize = strlen( $gzfile );
+        } else {
+            $filesize = filesize( $upload['file'] );
+        }
 
 		if ( isset( $headers['content-length'] ) && $filesize != $headers['content-length'] ) {
 			@unlink( $upload['file'] );